Presently, overtwistedness in high dimensions is not understood, if such a concept exists at all. To justify our use of terminology, we argue that generally there can only be one flexible class of Legendrian knots. Let \((Y, \xi )\)  be a high dimensional contact manifold which is “overtwisted”. Let \(L\)  be a loose Legendrian knot, and suppose \(L_{OT}\)  is in the same formal isotopy class, and has overtwisted complement. Since an \(M\) -stabilization takes place in a small neighborhood of a point, \(L^\prime = s_{S^1 \times D^{n-1}}(L_{OT})\)  is a loose knot, whose complement remains overtwisted. By Theorem  REF , \(L\)  is Legendrian isotopic to \(L^\prime \) . If knots with overtwisted complement have flexibility properties (as in  [1]} or  [2]} in the \(n=1\)  case), \(L_{OT}\)  should be ambient isotopic (or at least contactomorphic) to \(L^\prime \) . Thus in a hypothetical high dimensional overtwisted manifold, we expect a Legendrian knot is loose exactly when it has overtwisted complement.
